While i absolutely agree with your gut feelings, the logic behined the "Those societies [ancient Greece and the Roman Republic] were far from being democratic. Power was held by an oligarchy of patricians who ruled plebeian and slave classes." part is flawed:
The term 'democracy' has primarily been defined against the state organization used by the ancient Athenians (and about 80 other democratic cities that Plato described, but the manuscripts describing them have long been lost). So it is a strong contradiction to not call these sociaties democratic. Propably you give a more wider meaning to democrarcy.
Actually this is a common fallacy we often do. First we tend to attribute moral value to state systems, democracy is good, oligarchy is bad, benevolent dictatorship is better, and so on (see Cornelius Castoriadis). Often we promote democracy to the top of the list and eventually we expect everything from it! Wel, that's actually utopia, not democracy.
Democracy was never meant to be applied to all (men, women, rich, slaves, dogs, sheeps, trees and houses). This is a complete different topic; the catholicity of a democracy, which is part of the human rights appendix of democracy. And indeed, the later notions are contradictory to democracy, that somehow we, as humans, have to compromise!
(for instance, we all agree that dogs are not citizens, so we should be allowed to exterminate them with no penalty...or shouldn't we?)
In principal, you can have a democratic way of ruling for an organization (either a revolutionaly party, or a business company, or a city, or a planet) and at the same time, not to allow anyone from outside to participate to your decision-making process. The definition of the outsiders is a very controversial issue.
And think about it for a while: When Athenians devised democracy, they had slaves, as many other cities did, and yet, they were the ones to discover democracy, not the citizens from other cities! Why?
Ancient Rome is a totally different story! It is a republic, not a democracy! Expect all kinds of differencies here. Apart from the fact that the public did not govern, the public-related decision-making processes were based mostly on majority and voting, while in ancient Athens, the sortion was a widespread tactic (see Athenian democracy).